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The Gas Laws

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Kinetic Molecular Theory (KMT) Particles of matter are always in motion Helps to explain differences between the 3 physical state Helps to explain properties of the 3 physical states

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Solids Definite shape and volume Particles packed together in fixed positions Strong attraction between particles Very little kinetic energy Cant be compressed

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Liquids Definite volume - meniscus indicates volume Takes some shape of container Particles close but can move; less attraction between particles More kinetic energy than solid Cant be compressed

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Gases - Part 1 Ideal - follows all KMT assumptions No definite shape - takes shape of container; fills container completely No definite volume - takes containers complete volume No attraction between particles Most kinetic energy - in constant motion - but KE depends on temperature Collide between gas molecules creates pressure. More collisions = more pressure Collisions are elastic – gas molecules bounce off each other and do not react

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Ideal Gases - Part 2 Gases can be compressed. Small number of particles within large volume of space Can diffuse - particles spread out to fill space Can effuse - pass through small openings Low density – small mass/large volume (which is why most float)

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Equivalent Gas Pressures 1 atm (atmosphere) - force of atmosphere pressing down at sea level and 0ºC 760 mm Hg - height of Hg column at sea level and 0ºC (or 29.92 in Hg) 760 torr - same as mm Hg 14.7 psi (pounds/in 2 ) 1.013 bars (or 1013 mbars) 101.325 kPa (or 101325 Pa) - force/area

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Measuring Gas Pressures - Part 1 As air pushes downward, its force (pressure) pushes Hg up into the tube. Measuring the height of the Hg column in the tube measures the air pressure in mm Hg or torr

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Measuring Gas Pressures - Part 2 (A) Absolute pressure (how a barometer works; air is the gas) (B) P atm > P gas because the Hg is higher on gas (weaker) side (C) P atm < P gas because the Hg is higher on air (weaker) side

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The ABCD Gas Laws A = Avogadros Law 2 gases at the same temperature and pressure have equal volumes and equal number of molecules Molar volume: 22.4 L of any gas at STP has 6.02 x 10 23 molecules

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The ABCD Gas Laws B =Boyles Law Relationship between gas volume (V) and pressure (P) when temperature (T) and moles of gas (n) are constant Equation: P 1 V 1 = P 2 V 2 Or to solve for V2, use

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Boyles Law As the piston pushes downward, pressure increases from P 1 to P 2. Volume decreases from V 1 to V 2 So when P increases, V decreases. This is an INVERSE (or INDIRECT) relationship

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Boyles Law Graph Pressure (mm Hg)LowHigh VolumeVolume Low High P and V

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Boyles Law Real Life Applications Lung Ventilation (Inhale/Exhale) Drinking from a straw Spray cans

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The ABCD Gas Laws C = Charles Law Relationship between gas volume (V) and temperature (T) when pressure (P) and moles of gas (n) are constant V 1 = V 2 or T 1 T 2 Temperatures must be in ºK (ºC + 273 = ºK)

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Charles Law As temperature increases, the molecules gain energy, move faster and spread out, so volume increases Since both temperature and volume are changing in the same direction it is a DIRECT relationship. Pressure remains constant (10 N) Number of particles remains constant

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Charles Law Graph High Low Temperature (ºK) VolumeVolume T and V

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Charles Law Real Life Application Hot air balloons - hot air rises because volume goes up with temperature. The hot air is less dense (same mass but more volume) and so it rises.

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The ABCD Gas Laws D = Daltons Law In a mixture, every gas exerts its own pressure called its PARTIAL PRESSURE The total pressure in the atmosphere (or container) is the sum of all the partial pressures P total = P 1 + P 2 +P 3 etc. Dalton also proved atoms existed

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Daltons Law of Partial Pressures

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Gay-Lussacs Law Relationship between gas temperature (T) and pressure (P) when moles of gas (n) and volume (V) are constant P 1 = P 2 or P 1 T 2 = P 2 T 1 T 1 T 2 Temperatures must be in ºK (ºC + 273 = ºK)

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Temperature (K) LowHigh Low Pressure Gay-Lussacs Law Graph T P Looks a lot like the graph for Charles law Direct relationship

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Gay-Lussacs law Real Life Applications Inner tube for tires. Gas cant escape so volume is constant…unless the pressure gets too high and then it… Gas confined in compressed gas tank

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Combined Gas Law Combines both Boyles and Charles Laws More realistic - gas pressure and temperature can both be changing and affecting volume Temperatures must be in °K Which – temperature or pressure – affects volume most? Depends on which undergoes greatest change

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Combined Gas Law Equation P 1 V 1 = P 2 V 2 T 1 T 2 or P 1 V 1 T 2 = P 2 V 2 T 1 To solve for V 2 use:

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Combined Gas Law – Example Problem A weather balloon containing helium with a volume of 410.0 L rises in the atmosphere and is cooled from 27 ºC to –27 °C. The pressure on the gas is reduced from 110.0 kPa to 25.0 kPa. What is the volume of the gas at the lower temperature and pressure? V 1 = 410.0 L P 1 = 110.0 kPa T 1 = 27 °C V 2 = ? P 2 = 25.0 kPa T 2 = -27 °C + 273 = 300 K+ 273 = 246 K

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P 1 V 1 = P 2 V 2 T 1 T 2 P 1 V 1 T 2 = P 2 V 2 T 1 110.0 kPa x 410.0 L x 246 K = 25.0 kPa x V 2 x 300 K 25.0 kPa x 300 K 25.0 kPa x 300 K 1479.28 L = V2 1480 L (3 s.d.)

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Ideal Gas Law Combines the ABC laws (Avogadros, Boyles, and Charles) Not only temperature, pressure, and volume change, but also moles Can be used to determine gas density, mass, and molar mass

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Ideal Gas Law Equation PV = nRT P = Pressure at standard pressure V = Volume at STP n = moles at STP T = Temperature at standard temperature So whats R?

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R – The Gas Constant PV = nRT P = Pressure at standard pressure (1 atm) V = Volume at STP (22.4 L) n = moles at STP (1 mole) T = Temperature at standard temperature (273 K) PVnTPVnT 1 atm x 22.4 L 1 mole x 273 K 0.0821 atmL moleK = R Notice how R contains all the units for the variables. Rs value will only change if the pressure units change = R

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R – The Gas Constant other values If pressure is measured in mm Hg (or torrs): 62.4 mmHgL moleK If Pressure is measured in kPa: 8.31 kPaL moleK If Pressure is measured in mbar: 83.1 mbarL moleK If Pressure is measured in atm: 0.0821 atmL moleK

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Ideal gas law – example problem A 500. g block of dry ice [CO 2 (s)] becomes a gas at room temperature. What volume will the dry ice have at room temperature (25°C) and 975 kPa? PV = nRT P = 975 kPan = 500.g/molar mass CO 2 V = ?R = use kPa version T = 25°C (change to °K)

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PV = nRT P = 975 kPan = 11.36364 molesCO 2 V = ?R = 8.31 kPaL/mole°K T = 298°K 975 kPaV = (11.36364 mole)(8.31 kPaL/moleK)(298°K) 975 kPaV = (11.36364 mole)(8.31 kPaL/mole°K)(298°K) 975 kPa975 kPa V = 28.86 L V= 28.9 L (3 s.d.)

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Grahams Law of Effusion Diffusion of Gases Gases effuse – pass through small openings Gases diffuse – spread out from areas of high concentration to low concentration Diffusion rate depends on kinetic energy and molar mass

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Grahams Law – Part 2 Two gases at same temperature have same average kinetic energy, therefore… Speed of diffusion and effusion depends on molar mass Heavy gases are slow, light gases are fast (inverse relationship) Velocity fast Velocity slow =

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Oxygen has the highest molar mass, so it has the slowest speed. Hydrogen has the smallest molar mass; it is the fastest.

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Grahams Law – Example Problem #1 Determine the ratio of velocities for H 2 O and CO 2 at the same temperature. Determine the molar masses and which gas is fastest. Molar Mass H 2 0 2 H = 2.0 g 1 O = 16.0 g 18.0 g/mole Molar Mass CO 2 1 C = 12.0 g 2 O = 32.0 g 44.0 g/mole Light and Fast Slow and Heavy

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Velocity fast Velocity slow = Velocity H2O Velocity CO2 ===1.56 So H 2 O is 1.56 x faster than CO 2 So if H 2 O is 1.56 x faster than CO 2 – what is the CO 2 s velocity if the H 2 O has a velocity of 6.04 m/sec?

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Velocity H2O Velocity CO2 =1.56 6.04 m/sec Velocity CO2 = 1.56 6.04 m/sec 1.56 =Velocity CO 2 3.87 m/sec =Velocity CO 2

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